Harmonic Forms

De Rham Cohomology - Related Ideas - Harmonic Forms ... See also Harmonic differential If is a compact Riemannian manifold, then each equivalence class in contains exactly one harmonic form ... ω of a given equivalence class of closed forms can be written as where is some form, and γ is harmonic Δγ=0 ... Any harmonic function on a compact connected Riemannian manifold is a constant ...

Hodge Dual - Hodge Star On Manifolds - The Codifferential ... the exterior derivative, in that where ζ is a (k+1)-form and η a k-form ... This identity follows from Stokes' theorem for smooth forms, when i.e ... the appropriate topological vector spaces as closures of the spaces of smooth forms) ...

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